Maximize Inscribed Rectangle Area in a Semicircle

This example explores the area of rectangles inscribed in a semicircle to find the maximum area among all such rectangles. It visually demonstrates how the area changes as the rectangle's position is adjusted dynamically. Key mathematical concepts involved include optimization problems in calculus, the application of derivatives, and geometric constructions in coordinate geometry. The construction uses GeoGebra commands like Point, Semicircle, Line, Intersect, and Polygon to build and solve the vertices' coordinates and the area function of the inscribed rectangle. Suitable for high school and above students to understand the application of calculus in geometric optimization problems and coordinate geometry drawing techniques.